1. Suppose that the population of a certain type of bacteria, P. changes with time, t, according to the Limited Growth Model given by = k(M - P), P(0)= 10 million bacteria. %3D dt (a) Use the separation of variables method to find a formula for the population as a function of time. Assume that the initial population increases to 15 million bacteria after 0.5 hours, and that the carrying capacity of the system, M, is 20 million bacteria. (b) Check your particular solution. (c) Find the equilibrium population value(s) for this system, and determine their stability. (d) Find the change in population betweent-1 and t=2 hours using a definite integral.

1. Suppose that the population of a certain type of bacteria, P. changes with time, t, according to the Limited Growth Model given by = k(M - P), P(0)= 10 million bacteria. %3D dt (a) Use the separation of variables method to find a formula for the population as a function of time. Assume that the initial population increases to 15 million bacteria after 0.5 hours, and that the carrying capacity of the system, M, is 20 million bacteria. (b) Check your particular solution. (c) Find the equilibrium population value(s) for this system, and determine their stability. (d) Find the change in population betweent-1 and t=2 hours using a definite integral.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

1. Suppose that the population of a certain type of bacteria, P. changes with time, t, according to the Limited Growth
Model given by = k(M - P), P(0)= 10 million bacteria.
%3D
dt
(a) Use the separation of variables method to find a formula for the population as a function of time. Assume that
the initial population increases to 15 million bacteria after 0.5 hours, and that the carrying capacity of the
system, M, is 20 million bacteria.
(b) Check your particular solution.
(c) Find the equilibrium population value(s) for this system, and determine their stability.
(d) Find the change in population betweent-1 and t=2 hours using a definite integral.

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